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Continuous maximal regularity and analytic semigroups

Pages: 963 - 970, Issue Special, September 2011

 Abstract        Full Text (327.9K)              

Jeremy LeCrone - Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States (email)
Gieri Simonett - Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States (email)

Abstract: In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity for a closed operator $A$ : $E_1 \to E_0$ implies that $A$ generates a strongly continuous analytic semigroup on $E_0$ with domain equal $E_1$.

Keywords:  Maximal regularity, analytic semigroups, parabolic problems.
Mathematics Subject Classification:  Primary: 35K90, 47D06; Secondary: 35K35.

Received: July 2010;      Revised: March 2011;      Published: October 2011.